This article is on the inverse Galois problem in Galois theory of linear iterative differential equations in positive characteristic. We show that it has an affirmative answer for reduced algebraic group schemes over any iterative differential field which is finitely generated over its algebraically closed field of constants. We also introduce the notion of equivalence of iterative derivations on a given field—a condition which implies that the inverse Galois problem over equivalent iterative derivations are equivalent.

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作为迭代微分伽罗瓦群的约简群方案

本文是关于正特性线性迭代微分方程伽罗瓦理论中的逆伽罗瓦问题。我们表明，它对任何迭代微分域上的约简代数群方案都有肯定的答案，该域是在其代数闭常数域上有限生成的。我们还介绍了给定域上迭代推导等价的概念——这个条件意味着等价迭代推导上的逆伽罗瓦问题是等价的。